﻿<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<!--

    Webpage by Matthew Fisher

-->
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<title>Matt's Webcorner - Publications</title>
<meta name="keywords" content="Matthew Fisher, Publications, Computer Graphics, SIGGRAPH, research" />
<meta name="description" content="Publication List for Matthew Fisher" />
<link rel="stylesheet" type="text/css" href="default.css" />
</head>
<body>

<div id="upbg"></div>

<div id="outer">


	<div id="header">
		<div id="headercontent">
			<h1><font face="georgia">Matt's Webcorner</font></h1>
			<h2>Stanford 2014</h2>
		</div>
	</div>

	<div id="menu">
		<ul>
			<li><a href="index.html" >Home</a></li>
			<li><a href="projects.html" >Projects</a></li>
			<li><a href="publications.html" class="active">Publications</a></li>
			<li><a href="recipes.html" >Recipes</a></li>
			<li><a href="contact.html" >Contact</a></li>
		</ul>
	</div>
	<div id="menubottom"></div>

	
	<div id="content">
<div id="normalcontent">

<div id="mainD">
<div id="contentD">
<div id="headerD">
<h1>An Algorithm for the Construction of Intrinsic Delaunay Triangulations</h1>
<div id="authorsD">
<span>
<a href="http://graphics.stanford.edu/~mdfisher/publications.html">Matthew Fisher</a>
<sup>1</sup>
</span>
<span>
<a href="http://page.math.tu-berlin.de/~springb/">Boris Springborn</a>
<sup>2</sup>
</span>
<span>
<a href="http://page.math.tu-berlin.de/~bobenko/">Alexander Bobenko</a>
<sup>2</sup>
</span>
<span>
<a href="http://www.multires.caltech.edu/pubs/pubs.htm">Peter Schröder</a>
<sup>3</sup>
</span>
</div>
<div id="affiliationsD">
<span>
<sup>1</sup>
Stanford University
</span>
<span>
<sup>2</sup>
Technical University of Berlin
</span>
<span>
<sup>3</sup>
California Institute of Technology
</span>
</div>
<div id="centerpieceD">
<img id="teaserD" src="papers/intrinsicDelaunayTeaser.png"/>
<span>SIGGRAPH 2006</span>
</div>
<div id="gutsD">
<div id="abstractD">
<h2>Abstract</h2>
<br/>
<p>
The discrete Laplace-Beltrami operator plays a prominent role in many Digital Geometry Processing applications ranging from denoising to parameterization, editing, and physical simulation. The standard discretization uses the cotangents of the angles in the immersed mesh which leads to a variety of numerical problems. We advocate use of the intrinsic Laplace-Beltrami operator. It satisfies a local maximum principle, guaranteeing, e.g., that no flipped triangles can occur in parameterizations. It also leads to better conditioned linear systems. The intrinsic Laplace-Beltrami operator is based on an intrinsic Delaunay triangulation of the surface. We give an incremental algorithm to construct such triangulations together with an overlay structure which captures the relationship between the extrinsic and intrinsic triangulations. Using a variety of example meshes we demonstrate the numerical benefits of the intrinsic Laplace-Beltrami operator.
</p>
</div>
<div id="extrasD">
<h2>Extras</h2>
<br/>
<p class="item">
Paper: <a href="papers/intrinsicDelaunay.pdf"><img src="Images/pdf-icon.png"/>PDF</a>
</p>
<p class="item">
Google Scholar: <a href="http://scholar.google.com/citations?view_op=view_citation&hl=en&user=PUSWc4EAAAAJ&citation_for_view=PUSWc4EAAAAJ:Tyk-4Ss8FVUC"><img src="Images/google-icon.png"/></a>
</p>
<div class="item">
BibTeX citation:
<div class="bibtexD">
@inproceedings{fisher2006algorithm,
<br/>
  title={An algorithm for the construction of intrinsic Delaunay triangulations with applications to digital geometry processing},
<br/>
  author={Fisher, Matthew and Springborn, Boris and Bobenko, Alexander I and Schroder, Peter},
<br/>
  booktitle={ACM SIGGRAPH 2006 Courses},
<br/>
  pages={69--74},
<br/>
  year={2006},
<br/>
  organization={ACM}
<br/>
}
<br/>
</div>
</div>
</div>
<div id="clearfloatsD"></div>
</div>
</div>
</div>
	</div>

	<div id="footer">
			<div class="left">&copy; 2014 Matthew Fisher. All rights reserved.</div>
			<div class="right"><a href="http://www.nodethirtythree.com/">NodeThirtyThree Design</a></div>
	</div>
	
</div>

</body>
</html>

